void
MisesMat :: giveFirstPKStressVector_3d(FloatArray &answer,
GaussPoint *gp,
const FloatArray &totalDefGradOOFEM,
TimeStep *tStep)
{
MisesMatStatus *status = static_cast< MisesMatStatus * >( this->giveStatus(gp) );
double kappa, dKappa, yieldValue, mi;
FloatMatrix F, oldF, invOldF;
FloatArray s;
F.beMatrixForm(totalDefGradOOFEM); //(method assumes full 3D)
kappa = status->giveCumulativePlasticStrain();
oldF.beMatrixForm( status->giveFVector() );
invOldF.beInverseOf(oldF);
//relative deformation radient
FloatMatrix f;
f.beProductOf(F, invOldF);
//compute elastic predictor
FloatMatrix trialLeftCauchyGreen, help;
f.times( 1./cbrt(f.giveDeterminant()) );
help.beProductOf(f, status->giveTempLeftCauchyGreen());
trialLeftCauchyGreen.beProductTOf(help, f);
FloatMatrix E;
E.beTProductOf(F, F);
E.at(1, 1) -= 1.0;
E.at(2, 2) -= 1.0;
E.at(3, 3) -= 1.0;
E.times(0.5);
FloatArray e;
e.beSymVectorFormOfStrain(E);
FloatArray leftCauchyGreen;
FloatArray leftCauchyGreenDev;
double leftCauchyGreenVol;
leftCauchyGreen.beSymVectorFormOfStrain(trialLeftCauchyGreen);
leftCauchyGreenVol = computeDeviatoricVolumetricSplit(leftCauchyGreenDev, leftCauchyGreen);
FloatArray trialStressDev;
applyDeviatoricElasticStiffness(trialStressDev, leftCauchyGreenDev, G / 2.);
s = trialStressDev;
//check for plastic loading
double trialS = computeStressNorm(trialStressDev);
double sigmaY = sig0 + H * kappa;
//yieldValue = sqrt(3./2.)*trialS-sigmaY;
yieldValue = trialS - sqrt(2. / 3.) * sigmaY;
//store deviatoric trial stress(reused by algorithmic stiffness)
status->letTrialStressDevBe(trialStressDev);
//the return-mapping algorithm
double J = F.giveDeterminant();
mi = leftCauchyGreenVol * G;
if ( yieldValue > 0 ) {
//dKappa =sqrt(3./2.)* yieldValue/(H + 3.*mi);
//kappa = kappa + dKappa;
//trialStressDev.times(1-sqrt(6.)*mi*dKappa/trialS);
dKappa = ( yieldValue / ( 2 * mi ) ) / ( 1 + H / ( 3 * mi ) );
FloatArray n = trialStressDev;
n.times(2 * mi * dKappa / trialS);
////return map
s.beDifferenceOf(trialStressDev, n);
kappa += sqrt(2. / 3.) * dKappa;
//update of intermediate configuration
trialLeftCauchyGreen.beMatrixForm(s);
trialLeftCauchyGreen.times(1.0 / G);
trialLeftCauchyGreen.at(1, 1) += leftCauchyGreenVol;
trialLeftCauchyGreen.at(2, 2) += leftCauchyGreenVol;
trialLeftCauchyGreen.at(2, 2) += leftCauchyGreenVol;
trialLeftCauchyGreen.times(J * J);
}
//addition of the elastic mean stress
FloatMatrix kirchhoffStress;
kirchhoffStress.beMatrixForm(s);
kirchhoffStress.at(1, 1) += 1. / 2. * K * ( J * J - 1 );
kirchhoffStress.at(2, 2) += 1. / 2. * K * ( J * J - 1 );
kirchhoffStress.at(3, 3) += 1. / 2. * K * ( J * J - 1 );
FloatMatrix iF, Ep(3, 3), S;
FloatArray vF, vS, ep;
//transform Kirchhoff stress into Second Piola - Kirchhoff stress
iF.beInverseOf(F);
help.beProductOf(iF, kirchhoffStress);
S.beProductTOf(help, iF);
this->computeGLPlasticStrain(F, Ep, trialLeftCauchyGreen, J);
ep.beSymVectorFormOfStrain(Ep);
vS.beSymVectorForm(S);
vF.beVectorForm(F);
answer.beVectorForm(kirchhoffStress);
status->setTrialStressVol(mi);
status->letTempLeftCauchyGreenBe(trialLeftCauchyGreen);
status->setTempCumulativePlasticStrain(kappa);
status->letTempStressVectorBe(answer);
status->letTempStrainVectorBe(e);
status->letTempPlasticStrainBe(ep);
status->letTempPVectorBe(answer);
status->letTempFVectorBe(vF);
}
